An optical fiber can guide light with multiple spatial patterns, each of which is uniquely designated as a transverse mode of the fiber (hereafter, called mode, for brevity). The dispersive characteristics of an optical signal in a fiber depend on the mode in which it is travelling. Thus, each mode may be characterised with a dispersion value specific to it. The dispersion of a mode is roughly equal to the sum of the material dispersion (Dm) and waveguide dispersion (Dw). The material dispersion is the dispersion of the material in which the optical signal resides—that is, the material of which the fiber is made (most commonly, Silica with trace amounts of Germanium, Phosphorus, Fluorine and other dopants). The waveguide dispersion is due to the refractive index profile that defines a fiber waveguide. Hence, the dispersion of a mode (Dtotal=Dm+Dw) can be designed by suitably altering the refractive index profile of the fiber (which modifies Dw). As will be explained below, for most optical fiber designs, the waveguide dispersion Dw, is negative. Hence, while the refractive index profile of a fiber can designed to obtain extremely large, negative values of Dw, and hence the fiber dispersion Dtotal, of varying negative magnitudes can be achieved, most fibers are bounded by the material dispersion, in maximum achievable dispersion. Silica, even with a variety of dopants, has Dm>0 for wavelengths greater than roughly 1300 nm, and has Dm<0 for wavelengths below 1300 nm. Hence, most optical fibers can achieve positive or negative dispersion (Dtotal) for wavelengths greater than 1300 nm, but possess only Dtotal<0 for wavelengths below 1300 nm.
The optical response of an optical pulse in a fiber depends critically on the dispersion it experiences. This is true for both linear effects such as pulse spreading, and nonlinear effects such as pulse distortion and soliton formation. Hence, the dispersion of a fiber plays a key role in designing fiber-based devices. Whereas optical fiber communications systems typically operate at 1300 nm or between 1500 and 1650 nm, many other important optical systems operate at lower wavelengths. A preferred wavelength of operation for fiber lasers is at 1060 nm. The ubiquitous titanium-doped sapphire laser, which is used in several pump-probe experiments as well as in biomedical imaging or therapy, typically operates in wavelength range of 700 nm to 1000 nm. Finally, all wavelengths visible to the human eye, and hence wavelengths at which several commercial gadgets such as the laser pointer work, spans the range of 400 to 700 nm. Common to all these applications is a wavelength of operation below 1300 nm, where the silica fiber offers only negative dispersion. Fibers that have positive or zero dispersion in these wavelength ranges would enable propagation of solitons and generate broadband supercontinua, of interest to biomedical imaging systems, for instance. For many of these systems, positive but low dispersion fibers are required at these wavelengths. Hence, there is a need for optical fibers that can provide stable propagation for optical pulses of wavelength less than 1300 nm, whose dispersion is positive and can be adjusted by suitably designing the refractive index profile. This requires a fiber whose waveguide dispersion Dw can be designed to be greater than zero in any desired wavelength range.
Most optical fibers are single-moded, which means that they support only the lowest order, fundamental mode, also designated as the LP01 mode. The two numerals in the subscript refer to the number of intensity minimas (zeroes) the spatial light pattern has, in the azimuthal (1st subscript) and radial (2nd subscript) directions, respectively. As mentioned earlier, the LP01 in standard silica fibers where the refractive index profile is defined by various dopants to silica, can achieve only Dw<0. Thus, the entire class of these fibers can have a maximum Dtotal=Dm, the material dispersion of silica. Since Dm<0 for wavelengths<1300 nm, it is not possible to achieve Dtotal>0 in this wavelength range.
Fibers that contain air holes that extend longitudinally along the axis of the fiber (called air-silica fibers, hereafter) possess interesting properties, as described by J. C. Knight and coworkers in volume 12, page 807 of the July 2000 issue of the IEEE Photonics Technology Letters, entitled “Anomalous Dispersion in Photonic Crystal Fiber.” They demonstrate that air-silica fibers can achieve large positive dispersion in any wavelength range. However, the dispersion of air-silica fibers is closely tied to their modal areas, and it is not possible to achieve high dispersion as well as large effective modal areas—hence, this design space would be of limited use in systems requiring high positive dispersion but also low nonlinearities. In addition, these fibers are known to have high birefringence and loss, both of which diminish their utility in practical systems. Moreover, an all-solid fiber made by conventional technology will always be cheaper than fibers that require manual assembly of the fiber preforms (as is the case with air-silica fibers). These fibers also have termination problems—splices to other fibers lead to loss, changes in optical properties, and cannot be made reliably.
Lysiansky, Rosenblit and Wei disclosed an alternative technique to obtain Dw>0. In U.S. Pat. No. 6,724,964, they disclosed exemplary refractive index profiles of a solid (i.e. not air-silica) fiber that supports higher order modes (HOM) in addition to the LP01 mode, where the waveguide design yields dispersion greater than +50 ps/nm-km for the LP02 or LP03 mode. However, these designs do not enable achieving zero or low positive dispersion values in the wavelength range<1300 nm, and hence cannot be utilized for applications such as soliton compression and supercontinuum generation, typically exploited with lasers in the wavelength range of 700-900 nm. In addition, these HOM fibers suffer from a severe drawback common to most fibers that support more than a single mode. While it is desired to have light residing substantially in the desired HOM, the presence of other modes makes such designs susceptible to mode coupling, by which process light can either be lost or can cause deleterious interference-noise problems. Such mode coupling increases as the difference in effective index (neff) between the desired modes and any other mode, decreases. The design space disclosed by the above authors leads to identical neff for the LP02 and LP11 modes, at the operation wavelengths. Hence these designs are especially susceptible to both interference noise and loss.
Hence, there exists the need for a fiber that can be manufactured by conventional fabrication techniques, whose refractive index profile is such that it yields not only positive dispersion of any magnitude in any wavelength range, but also ensures that the modal spacings in the fiber are such that the fiber is not susceptible to mode coupling.